Find the equation of the perpendicular bisector of the line segments wit endpoints (1,2) and (6,12)?

Question

Please show me how u got that or in detailed info! Thanks!

Answer 1

The gradient of the line is

M = (y2-y1)/(x2-x1)

= 12 - 2 / 6 -1

= 10 / 5

= 2

So the gradient of the perp bi is -1/2

The midpoint is (1+6)/2 , (2 + 12)/2

= (3.5,7)

So the eqn of the line is:

Y - b = m(x-a)

Y - 7 = -1/2(x-3.5)

Y - 7 = -1/2x + 1.75

Y = -1/2x + 8.75

OR

Y = -1/2x + 35/4

Hope this helps!

Answer 2

To get from (-2, 3) to (2, 5) you go best 4 and up 2 so the midpoint is sweet 2 and up a million -- the factor (0, 4) The slope of the line by using the two given factors is m = 2/4 = a million/2. The slope of the line this is perpendicular is the unfavorable reciprocal m = -a million/a million/2 = -2 y = -2x + b the place x = 0 and y = 4: 4 = -2(0) + b b = 4 The equation of the perpendicular bisector is: y = -2x + 4

Answer 3

First, find the slope of the line segment.

m = Δy/Δx = (12-2)/(6-1) = 10/5 = 2

The slope of a line perpendicular to this will be the negative reciprocal which is -1/2.

Next, find the midpoint P between the endpoint of the line segment.

P = {(1+6)/2,(2+12)/2} = (7/2,7)

Now plug into the formula for the perpendicular bisector.

y - 7 = (-1/2)(x - 7/2)
y = (-1/2)x + 7/4 +7
y = (-1/2)x + 35/4

Answer 4

If I'm understanding this, you want a value for the point at which the perpendicular bisector cuts the line segment in half forming 90 degree angles.

To get that, add the two "x" values (1+6) and divide by 2 = 3.5
Add the two "y" values (2+12) and divide by 2 =7

That makes the fomula.

[(1+6)/2,(2+12)/2] = (3.5,7)